Gems are set correctly, but then do not appear in the list of gems

Question

Gems are set correctly, but then do not appear in the list of gems

I recently switched from rvm to rbenv to control Ruby versions, and since I ran into all the gem issues. If I run gem list, it displays only about 10 gems, all of which are system defaults. But when I run bundle installin a project with a Gemfile, it lists a ton of other gems and says that they were successfully installed. Then I can not start them from the command line or require them in ruby files!

Exit from gem list:

*** LOCAL GEMS ***

bigdecimal (1.2.0)
io-console (0.4.2)
json (1.7.7)
minitest (4.3.2)
psych (2.0.0)
rake (0.9.6)
rdoc (4.0.0)
rubygems-update (2.3.0)
test-unit (2.0.0.0)

And then from bundle install

Using i18n 0.6.9
Using json 1.8.1
Using minitest 5.3.5
Using thread_safe 0.3.4
Using tzinfo 1.2.1
Using activesupport 4.1.1
Using builder 3.2.2
Using activemodel 4.1.1
Using arel 5.0.1.20140414130214
Using activerecord 4.1.1
Using bond 0.5.1
Using rack 1.5.2
Using rack-protection 1.5.3
Using rack-test 0.6.2
Using ripl 0.7.1
Using ripl-multi_line 0.3.1
Using ripl-rack 0.2.1
Using shotgun 0.9
Using tilt 1.4.1
Using sinatra 1.4.5
Using sinatra-activerecord 2.0.2
Using sqlite3 1.3.9
Using tux 0.3.0
Using bundler 1.6.3
Your bundle is complete!

My gem envlooks like this:

 RubyGems Environment:
  - RUBYGEMS VERSION: 2.3.0
  - RUBY VERSION: 2.0.0 (2014-05-08 patchlevel 481) [x86_64-darwin13.2.0]
  - INSTALLATION DIRECTORY: /usr/local/var/rbenv/versions/2.0.0-p481/lib/ruby/gems/2.0.0
  - RUBY EXECUTABLE: /usr/local/var/rbenv/versions/2.0.0-p481/bin/ruby
  - EXECUTABLE DIRECTORY: /usr/local/var/rbenv/versions/2.0.0-p481/bin
  - SPEC CACHE DIRECTORY: /Users/Alex/.gem/specs
  - SYSTEM CONFIGURATION DIRECTORY: /usr/local/var/rbenv/versions/2.0.0-p481/etc
  - RUBYGEMS PLATFORMS:
    - ruby
    - x86_64-darwin-13
  - GEM PATHS:
     - /usr/local/var/rbenv/versions/2.0.0-p481/lib/ruby/gems/2.0.0
     - /Users/Alex/.gem/ruby/2.0.0
  - GEM CONFIGURATION:
     - :update_sources => true
     - :verbose => true
     - :backtrace => false
     - :bulk_threshold => 1000
     - "gem" => "--no-rdoc --no-ri"
  - REMOTE SOURCES:
     - https://rubygems.org/
  - SHELL PATH:
     - /usr/local/var/rbenv/versions/2.0.0-p481/bin
     - /Users/Alex/.rbenv/libexec
     - /Users/Alex/.rbenv/bin
     - /usr/local/heroku/bin
     - /usr/local/var/rbenv/shims
     - /usr/bin
     - /bin
     - /usr/sbin
     - /sbin
     - /usr/local/bin
     - /Users/Alex/.dotfiles/bin